三次B样条小波的曲线拟合研究

A Research on Curve Fitting of Cubic B-spline Wavelets

针对拟合曲线的精度与光顺性互相冲突,在进行曲线拟合时常以牺牲一方面的质量来使另一方面满足要求的问题,提出了基于三次B样条小波的曲线拟合方法。对控制点坐标的数据信息进行小波处理,剔除高频细节信息,获取低频主体信息,用将近原始控制点一半数目的新的控制点来表示原始控制点的数据特征,既保证了拟合精度又提高了拟合光顺性,从而提高了数控加工的精度。经实例验证,该方法行之有效,为曲线拟合提供了一种兼顾拟合精度、光顺性与加工精度的方法。

Due to the conflict between the accuracy of the curve fitting and the smoothness,which most of time sacrifices the quality of one aspect of the curve fitting to meet the requirement for another when the curve fitting is conducted,the curve fitting method based on the cubic B-spline wavelet transform is put forward. The data on original control points are processed with the wavelet transform,information on high frequency detail is removed to obtain principal information on low frequency. The new control points are used to represent the data characteristics of the original control points,thus ensuring the precision and improving the smoothness of the curve fitting and the machining accuracy. The case studies show that the curve fitting method is effective and provides a compromise method for the curve fitting between fitting precision,smoothness and machining accuracy.